WARSAW, April 14 (Reuters) - When Polish deputy prime minister Elzbieta Bienkowska applied to study at a prestigious university in Warsaw, she was rejected after one of the interview panel questioned how she could study and raise a family as well.

The next year, she applied again and was asked the same thing. She replied by inquiring if the panel would put that question to male applicants. She was accepted.

Now, two decades later, Bienkowska has emerged as one of Poland's most visible politicians and a potential candidate to succeed Prime Minister Donald Tusk if, as many people anticipate, he steps down in the next few years.

The question of Tusk's heir apparent is a crucial one for investors because, unlike his predecessors, he has been able to bring stability to the fractious political landscape, helping to ensure growth in the eastern European Union's biggest economy.

If Bienkowska, 50, does replace him, she is likely to be single-minded and determined, as suggested by the story of her university application, which was recounted to Reuters by her office and corroborated by a former university classmate.

But little is known about her political convictions and she has no power base within the ruling party, prompting some people to believe she will have to rely on Tusk for her authority, even if she takes over his job.

"She is a woman who gets things done, very technocratic, practical, a professional," said a former government minister, who did not want to be identified.

"It looks like Tusk is grooming her to replace him at some point, when he decides it is time."

IRONING

Tusk has said he will lead his party into the next parliamentary election, in 2015, and has left open the question of what happens after that. Polish media speculate he may land an important job at EU headquarters in Brussels.

If she were to become prime minister, Bienkowska, who declined to be interviewed for this article, would be the second woman to do the job in Polish history after Hanna Suchocka in the early 1990s.

Asked if she wanted to be premier, her office referred to past interviews with Polish media in which, in response to the same question, she had said she was a technocrat and focused on completing the tasks she had been assigned.

Bienkowska was born in the southern Polish city of Katowice, and studied Farsi as an undergraduate. By the time she applied, several years later, to do the masters at Warsaw's National School of Public Administration, she had two small children.

She stood out there because she was older than many students and already had a family. The former classmate recalled that in English classes, the teacher asked students to say what their hobbies were.

"Everybody was joking around, saying things like sex, drugs and rock 'n roll, and she said ironing," said the ex-classmate, who did not want to be named because he is now a public servant.

After her masters degree, Bienkowska took a job in local government in Katowice, then worked her way up to head the development department in the regional government.

In 2007, the newly-elected prime minister named Bienkowska, who now has three children, as minister for regional development. Her appointment coincided with the arrival of vast sums of EU aid designated for development projects.

The amount involved was nearly 68 billion euros ($94.44 billion) for the period 2007-2013, and it was Bienkowska's job to decide to which projects the money would be allocated.

During her tenure, Poland obtained new highways, new sports stadiums, and new public buildings.

She brought a fresh style. When Reuters interviewed her in her office last year, she kicked off her shoes under the desk and broke off to take a call from her daughter on her smartphone. A shawl covered a tattoo on her shoulder.

In November last year Transport Minister Slawomir Nowak, who many observers say was being groomed as Tusk's heir apparent, stepped down after an investigation was launched into how he came to have a $6,600 wristwatch.

In a reshuffle a few days later, Bienkowska was given the deputy prime minister's job and the new role of minister for infrastructure and development.

NEW SCRUTINY

Bienkowska brought to the new job a no-nonsense approach and time management skills, which, people who know her say, comes in part from juggling work and family responsibilities in a way most Polish men don't have to.

On one occasion, she stood in for the absent prime minister to chair a meeting of the cabinet. Asked if Bienkowska had run the meeting any differently from usual, a serving official who was present said: "Yes, it was shorter."

She is now under more scrutiny. Her biggest public misstep to date came in January when she appeared on television to talk about how some passenger trains were delayed for hours in wintry conditions.

Her phrase "Sorry, that's the climate we have," was seized on by critics as flippant and uncaring. It was parodied endlessly on the Internet, with one rap artist sampling the phrase in the chorus of a satirical song.

However, Bienkowska has won popularity with voters by keeping aloof from party politics. She is not a member of Tusk's Civic Platform party, and when she was elected to a seat in the upper house of parliament in 2011, she ran as an independent.

But people who know her say some members of Civic Platform don't warm to her outsider status. If she is anointed as Tusk's successor, she will owe her elevation in large part to his patronage. "With her at the helm, he will still have control," said the former minister. ($1 = 0.7201 Euros) (Additional reporting by Karolina Slowikowska; Editing by Mark Heinrich)

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